
where \(\phi _i\)  is an iid spatial random effect, \(\psi _i\)  is a structured spatial random effect, \(\upsilon _t\)  is an iid temporal random effect, \(\nu _t\)  is a structured spatial random effect, and \(\Phi _{it}\)  is a spatio-temporal interaction effect. The interaction effect has four types, depending on which of the two spatial effects and which of the two time effects interact. Structured random effects include random walk models, autoregressive processes, and correlated random effects of different dimensions. These different ways to specify the spatio-temporal structure of the model do not violate latent Gaussianity, and hence all posterior marginals of the model parameters can be fit using the INLA method [1]}.
